Viewing photo captions below the photo in Apple or third-party apps

On a Mac you can view the captions below the thumbnails if you open your Photos Library in PowerPhotos. The free trial version of PowerPhotos will suffice to be able to use PowerPhotos as a second browser window. It also offers a nice column view, so we can compare the metadata of photos or sort them by one of the columns.

As léonie says,  the trusted 3rd party app PowerPhotos ($35) is the best choice, since it is so useful for other things, too-- even the free version.

If you don't need the captions to update in real time, then another useful way to show captions, on the Mac, is to use Print>Contact Sheet.

You can choose different sizes of pictures, and different numbers per page.

And you get lots of options for what appears under the pictures:

And you don't have to actually print, of course. You can save the result as a PDF

and keep it for future reference.

I've used this to send copies of old pictures with my descriptions to other family members for comments.

Would this work for you?

Titles can be displayed under the image so one option is to copy Captions to Titles with an AppleScript (or exiftool before importing). ...but I wouldn't do that because many of my Captions are long or VERY long.

Are you asking about Photos for Mac? iPhone? iPad? What version(s)?

There are no third party apps that can use the iCloud Photo Library.